Abstract
The generalized k-connectivity \(\kappa _k(G)\) of a graph G, introduced by Hager (J Comb Theory 38:179–189, 1985) is a generalization of the classical connectivity \(\kappa (G)\) with \(\kappa _2(G)=\kappa (G)\). In this paper, we construct graphs to show that for every pair of integers m and \(n(1<n <m)\) there is a graph with the generalized 3-connectivity n whose line graph has the generalized 3-connectivity m.
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Authors are very grateful to the reviewers to give the extremely specialized comment.
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Communicated by Xueliang Li.
Supported by the National Science Foundation of China (Nos. 11661066, 11551001, 11161037, 11561056) and the Science Found of Qinghai Province (No. 2014-ZJ-907).
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Li, Y., Mao, Y. A Result on the 3-Generalized Connectivity of a Graph and Its Line Graph. Bull. Malays. Math. Sci. Soc. 41, 2019–2027 (2018). https://doi.org/10.1007/s40840-016-0441-0
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DOI: https://doi.org/10.1007/s40840-016-0441-0